2014 · Q33
Consider the following statements:
- 1No integer of the form 4k + 3, where k is an integer, can be expressed as the sum of two squares.
- 2Square of an odd integer can be expressed in the form 8k + 1, where k is an integer.
Which of the above statements is/are correct?
Elementary MathematicsNumber System
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
Squares mod 4 are 0 or 1, so a sum of two squares is never 3 mod 4; (2m+1)^2 = 4m(m+1)+1 = 8k+1 since m(m+1) is even.